All right then: What you saw was not a list of "approved" handguns, (we have no such list) but a catalog of primary issue handguns of the era, provided only for information. If you look in "GAF Class Structure and Battle rifle Standards", you will find this:
"-NOTE- Handguns are related IN PERIOD to the rifle used. It is understood that some handgun/rifle combinations may be difficult to impossible to achieve. Reasonable substitutions are allowed. Officers of the period often purchased their own sidearms. (Notice I say "Handguns"? Thats right. Broomhandle fanatics rejoice! For you DA revolver types, no loading aids of any type.) When in doubt, a single action revolver will always be acceptable."
Also:
" Handguns shall be Milspec, or of demonstrated military usage, related in period to the rifle used. "Period" shall be defined as related to the adoption date of the rifle. Civilian handguns shall be of appropriate period as determined by the rifle used.
Those wishing to use C&Bs may use 2 revolvers, charged and capped with 5 rounds each, carried in appropriate holsters. Targets not hit by these 10 rounds shall be made up with the longarm.
All Calibers in the Milspec class will be milspec, with case by case exemptions granted. (Example: a properly outfitted Winchester 95 carbine in .30-06 may be accepted in liu of the Milspec .30 US caliber)
All calibers will be loaded to CAS spec. Rifle calibers will be all lead, no more than 405 grains lead at no more than 1500 FPS. Calibers greater than .501 may use up to a 480 grain bullet. Gas checks may be used at the Match directors discretion on rifle calibers of .32 or less. (Call Ahead!) Hangun calibers all lead at no more than 1200 fps. Further requirements for minimum pistol loadings are under discussion and may be implemented should need be.
Handgun Calibers in "Civilian" classes ( Long action, Short action, Buffalo and Shotgunner ) will have a minimum bore diameter of .357. All Non Milspec handguns shall have a minimum bore diameter of .357. For competition purposes, the short action WCF calibers (.44-40, .38-40) shall be considered "Pistol" caliber."
Also:
"Note we often refer to handuns, not single action revolvers. It means just that. That they should be related in PERIOD to the rifle used in the Milspec classes gives a great deal of flexibility. MILITARY classes will be shot in accordance with Battle Rifle Standards"
Reasonable caliber substitutions are always allowed. A .38/.357 is considered a reasonable substitute for most handgun calibers as needed.
Finally, at the bottom of the "list", is this line:
"This is not an exclusive list, the GAF recognizes all milspec weapons of the period, both primary and secondary, as well as those of demonstrated military usage." (A .38 Single Action revolver is considered "of demonstrated military usage" for our purposes)
All of which is just a windy way of letting you know your .357 SA revolvers are just fine for GAF usage.